As a disclaimer I study law and not history, and my understanding of this subject comes primarily through the lens UK/Commonwealth legal history. There are two things that stand out about the series of attempts made on Queen Victoria's life during her early reign - firstly, the fact that these all appeared to be 'lone wolf' style attacks without any connection to politically motivated groups or terrorist organisations, and secondly, the way in which these would-be assassins were handled by the legal system. That's not to say that at least some of the men involved in these attempts did not have political or philosophical motives (Arthur O'Connor is known to have sympathised with Irish nationalism), but there is no evidence that they were active in radical circles, had connections with terrorist organisations, or plotted with other individuals prior to carrying out the attempt. What does link the majority of these men together is a history of mental health issues and/or low socioeconomic status - indeed, I'm almost reluctant to use phrases like 'assassination attempt' or 'attack' because when these cases went to trial, there was invariably some dispute as to whether the gun used was loaded with ball, or even capable of being fired at all.

This brings me to the second key point that marks these cases as significant - unlike in other cases where an attempt was made on the life of the monarch (for example Alexander II of Russia), the British authorities actively sought to downplay the significance of each attempt following the first one, with a view to chastising and humiliating the perpetrator rather than bringing down the full force of the law upon them (i.e. an indictment for treason and the death penalty). None of the men who allegedly 'shot' at Victoria (or hit her with a walking stick) were executed for their crimes. Indeed, the law was altered after the second attempt so that the subsequent cases were tried on a lesser charge carrying a reduced penalty, to remove both the perceived incentive for copy-cat attacks, and to ameliorate the harshness of a mandatory capital sentence in circumstances where the accused was mentally ill and the attempt was doomed to fail from the outset (i.e. because the gun wasn't loaded).

So, if most of these men weren't acting in furtherance of a political goal for which they were willing to lay down their own lives (again, in contrast to the burgeoning radical movement in the Russian Empire), why did the government believe that the threat of a treason charge incentivised rather than dissuaded men from carrying out copy-cat attacks? That's due to the way in which the first prosecution was handled - a teenager, Edward Oxford, with a history of unstable behaviour, who seemed to positively enjoy the notoriety of being Victoria's 'assassin'. As the law was written in 1840, the only charge under which he could be prosecuted was that of high treason, which marked the case out for an enormous amount of public attention as it still carried the penalty of execution by hanging and beheading (having most recently been carried out some twenty years previously and generating significant controversy at the time). It quickly became apparent that Oxford was not affiliated with any terrorist organisation, that there was insufficient evidence to demonstrate that his gun was ever loaded or that he actually intended to harm the Queen, and that he was nothing more than a naive and somewhat egotistical teenager displaying signs of mental illness. After a highly publicised trial he was eventually acquitted on what would now be considered an insanity defence, and confined to a mental institution (although from a legal perspective it should strictly have been a full acquittal as the actus reus of the charge was not proven). Somewhat surprisingly, given the popular perception of Victorian psychiatry, he seems to have thrived in the institution and used his time there towards leisure and self-improvement, being helped in this regard by doctors who regarded him as 'sane' from the time of his admission. While it's not possible to engage in retrospective diagnosis with any degree of precision, it's certainly possible that he suffered from a mental illness from which recovery was possible (such as major depression) and that the hospital environment facilitated this recovery, or that he may have suffered from a personality disorder.

Regardless of the true nature of his condition, it was widely reported in the media that Oxford was having the time of his life in the asylum, enjoying a standard of comfort far beyond that of most of the working class and spending his days studying languages and painting. When two further, virtually identical attempts were made to 'shoot' Victoria in rapid succession, by young men from an impoverished background using makeshift weapons, the popular belief was that these attacks were merely a means to an end rather than serious attempts on her life, with the 'end' being either fifteen minutes of fame and a comfortable period of seclusion in a mental institution, or as a means to bring about their own deaths (the third man, John William Bean, expressed suicidal thoughts in the period leading up to the attempt, and eventually did commit suicide). Consequently, an Act was passed by Parliament creating a new and separate offence of 'disturbing' the Queen and the public peace to distinguish these kind of desperate acts from treason. All of the subsequent attempts to shoot at, or strike, the Queen were prosecuted under this Act, which carried a maximum penalty of a public whipping and transportation to Australia rather than a death sentence, even in cases where the act may have been in part motivated by Irish nationalist sentiments. By emphasising the irrational, unstable, or pathetic aspects of each man's character, this also served to minimise any public perception of danger (to the Queen and to society at large) from nonconformist political elements.

If you're interested to read more on this subject, particularly about the lives of the individual men who tried to kill Victoria and their subsequent fates (some of which are surprisingly wholesome and go against our presumptions about mental illness and criminality) then I recommend the book 'Shooting Victoria: Madness, Mayhem and the Modernisation of the Monarchy' by Paul Thomas Matthews.